Answer:
x = 1 ± 2i
Step-by-step explanation:
x² - 2x + 5 = 0 ( add 5 to both sides )
x² - 2x = - 5
Using the method of completing the square
add ( half the coefficient of the x- term)² to both sides
x² + 2(- 1)x + 1 = - 5 + 1
(x - 1)² = - 4 ( take square root of both sides )
x - 1 = ± [tex]\sqrt{-4}[/tex] = ± 2i ( add 1 to both sides )
x = 1 ± 2i ( that is the solutions are complex )
Answer:
[tex]x=1\pm2i[/tex]
or
[tex]x=1+2i[/tex]
[tex]x=1-2i[/tex]
Step-by-step explanation:
All equations of the form [tex]ax^2+bx+c=0[/tex] can be solved using the quadratic formula: [tex]x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
Quadratic formula gives two solutions, one when ± is addition add one when it is subtraction.
[tex]x^2-2x+5=0[/tex]
Equation is in standard form: [tex]ax^2+bx+c=0[/tex]
Substitute 1 from a, [tex]-2[/tex] for b, and [tex]5[/tex] for C in the quadratic formula, [tex]\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\times \:1\times \:5}}{2}[/tex]
Multiply -4 × 5:
[tex]x=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:1\cdot \:5}}{2}[/tex]
Add 4 + -20:
[tex]x=\frac{-\left(-2\right)\pm \:4i}{2}[/tex]
* the opposite of -2 is 2:
[tex]x=\frac{2\pm 4i}{2}[/tex]
Now, solve equation:
[tex]x=\frac{2+4i}{2}[/tex]
Divide 2 + 4i by 2:
[tex]x=1-2i[/tex]
_____________________________
Which two functions always Which two functions always share the domain (-∞, ∞) and range (-∞, ∞)?
linear
absolute value
quadratic
exponential
reciprocal
cubic
cube root
square root
Answer:
Linear.
Cubic.
Step-by-step explanation:
Two functions always share the domain (-∞, ∞) and range (-∞, ∞) are linear and cubic.
What is domain?" Domain is defined as the set of all input values in the given function."
What is range?" Range is defined as the set of all output values in the given function."
According to the question,
For linear function we can put all the real numbers for the independent variable 'x' that is ( -∞ , ∞).
Domain of a linear function = ( -∞ , ∞).
Output values of the linear function is set of all real numbers (-∞,∞).
Range of a linear function = (-∞,∞).
For cubic function
Cubic function is an odd polynomial . One end extends to +∞ and other end to -∞.
Domain and range of cubic function (-∞,∞).
Hence, two functions always share the domain (-∞, ∞) and range (-∞, ∞) are linear and cubic.
Learn more about domain and range here
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A parachutist's speed during a free fall reaches 55 meters per second. What is this speed in feet per second? At this speed, how many feet will the parachutist fall during 15 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answers
Explanation:
Explanation:50 m ≅164 ft (3s.f.)
Explanation:50 m ≅164 ft (3s.f.)50 m/s≅164 ft/s
Explanation:50 m ≅164 ft (3s.f.)50 m/s≅164 ft/sdistance after 20s:
Explanation:50 m ≅164 ft (3s.f.)50 m/s≅164 ft/sdistance after 20s:d=164 ft/s ⋅20s
Explanation:50 m ≅164 ft (3s.f.)50 m/s≅164 ft/sdistance after 20s:d=164 ft/s ⋅20s=3280 ft
follow me
Help help help please help
[tex] \frac{ {8}^{4} }{8 {}^{2} } \times 8 {}^{3} [/tex]
Cancel the fraction to simplify it.[tex]8 {}^{2} \times 8 {}^{3} [/tex]
Calculate the product[tex]8 {}^{5} [/tex]
Hope it helps...Put y + 3 = -3(x + 2) in slope-intercept form.
Answer:
[tex]y + 3 = - 3(x + 2) \\ y + 3 = - 3x - 6 \\ y = - 3x - 9[/tex]
What is 19% of 41?
(Simplify, no links)
Answer:
7.79
Step-by-step explanation:
19 percent of 41 is the same as 19 per hundred of 41. We can therefore make the following equation:
19/100 = X/41
To solve the equation above for X, you first switch the sides to get the X on the left side, then multiply each side by 41, and then finally divide the numerator by the denominator on the right side to get the answer. Here is the work to illustrate:
19/100 = X/41
X/41 = 19/100
X*41/41 = 19*41/100
X = 779/100
X = 7.79
The work above shows the long way to explain how to calculate 19 percent of 41 in order to give you a foundation and better understanding of how to calculate the percentage. In the future, you could use this simplified formula:
(Y * P)/100
In our problem "What is 19 percent of 41?", Y is 41 and P is 19:
(41 * 19)/100 = 7.79
And once again you see that the answer is 7.79.
Find the measure of the marked angles.
The measure of the angles is
___ degrees
Answer:
43 degrees
Step-by-step explanation:
The angles are vertical angles. All vertical angles are congruent meaning that these 2 expressions can be set equal to each other. Then, solve for x and finally plug x back in to get the answer.
First, set of the equation(4x+19)=(6x+7)
Then, subtract 7 from both sides4x+12=6x
Next, subtract 4x both sides12=2x
Finally, divide both sides by 2x=6
Now, we can plug 6 into the expression given to show that both angles are 43 degrees.
Rút gọn biểu thức √81a^6b^2
Answer:
English.........plzpzl
someon please helpppp!
Answer:
The equation you would graph would be y=-4 +x or y= x-4 (basically the same thing)
y=0 then x would equal 4
Step-by-step explanation:
y=-4+x x-y=4
0=-4+x -x -x
+4 +4 -y= 4-x
4=x /-1 /-1
y= x -4
What is the slope of a line which passes through points (-7,2) and (21,-10)?
The question gives us two points, (-7,2) and (21,-10), from which we can find the slope and later the equation of the line.
Finding the Slope
The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)
= (2 - (- 10)) ÷ (-7 - 21)
= - ¹²/₂₈
= - ³/₇
Checking my answer:
We can use the slope we found and a point to write the equation of a line. If the line passes through both points, then we calculated the slope correctly.
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:
⇒ y + 10 = - ³/₇ (x - 21)
To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.
Simplify 3c-9d+7c+5d
Answer:
10c - 4d
Step-by-step explanation:
Hey there,
Combine like terms
3c - 9d + 7c + 5d
3c + 7c - 9d + 5d
= 10c - 4d
Hope this helps you.
Let me know if you have any other questions :-)
How many points of intersection are there between the graphs of the hyperbola and ellipse?
3x2 – 4y2 + 4x – 8y +4= 0
3x2 + y2 + 4x – 3y +4= 0
A.0
B. 1
C. 3
D.4
The point of intersection is the point where two or more functions meet.
The graphs of the hyperbola and ellipse have 0 point of intersection
The given parameters are:
[tex]\mathbf{3x^2 - 4y^2 + 4x - 8y + 4 = 0}[/tex]
[tex]\mathbf{3x^2 + y^2 + 4x - 3y + 4 = 0}[/tex]
To determine the points of intersection, we simply equate both equations.
So, we have:
[tex]\mathbf{3x^2 + y^2 + 4x - 3y + 4 = 3x^2 - 4y^2 + 4x - 8y + 4 }[/tex]
Cancel out the common terms
[tex]\mathbf{y^2 - 3y = - 4y^2 - 8y }[/tex]
Collect like terms
[tex]\mathbf{y^2 +4y^2= 3y - 8y }[/tex]
[tex]\mathbf{5y^2= - 5y }[/tex]
Divide through by 5
[tex]\mathbf{y^2= - y}[/tex]
Divide through by y
[tex]\mathbf{y= -1}[/tex]
The system of equation does not give room to calculate the x-coordinate at the x-axis.
Hence, the graphs of the hyperbola and ellipse have 0 point of intersection
Read more about points of intersection at:
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Answer: 0
Explanation: Took the test
Point L is on line segment
K
M
‾
KM
. Given
L
M
=
2
LM=2 and
K
M
=
19
,
KM=19, determine the length
K
L
‾
.
KL
.
Answer:
k is the option that makes sense
Help
Dealing with corresponding write reasons as well pls
Answer:
X=60°
Step-by-step explanation:
A1=100° vertically opposite angles
100°=2x-20°
120°=2x
X=60°
Please help!!!
Which table represents a linear function?
Answer:
it should be D
Step-by-step explanation:
What are the coordinates of the office? Enter the coordinates like this: (x,y) without any spaces. *
Answer:
Step-by-step explanation:
(6,9) it think its that
Find the value of the expression if x = 2.1, z = -4.2 and b = -3.
|2x−z|+6b
Answer:
[tex]{ \tt{ |2x - z| + 6b}} \\ \\ \dashrightarrow \: { \tt{ |2(2.1) - ( - 4.2)| + 6( - 3) }} \\ \\ \dashrightarrow \: { \tt{ |8.4| - 18 }} \\ \\ { \boxed{ \boxed{ \tt{ \dashrightarrow \: \: - 9.6 \: \: }}}}[/tex]
Please help me fast I need to finish!!!!!!
Answer:
ans: The line passes through the point (0,13)
Step-by-step explanation:
(0,13) is Y-intercept
Answer:
The answer is C the line passes through (0,13)
Step-by-step explanation:
helpppppppppppppppppppppppppppppp meeeeeeeeeeeeeeeeeee plsssssssssssssssssssssss there is more but plss help mee
Sofia received a payment of $ 145 to take care of her neighbor Carmen's dogs for 5 days. Every day, the neighbor Carmen was paying him 6 dollars more than the day before. How much money did Sofia earn on the third day of work?
it is a problem of equations
please help me
Answer:
you betrayed me and i know that youll never feel srry
Step-by-step explanation:
27 is 45% of what number?
Answer:
60%
Step-by-step explanation:
The first step is to divide 27 by 45 to get the answer in decimal form:
27 / 45 = 0.6000
Then, we multiplied the answer from the first step by one hundred to get the answer as a percentage:
0.6000 * 100 = 60.00%
60
Step-by-step explanation:
If you take 45 percent of a number and get 27, then what is that number? In other words, you know that 45 percent of a number is 27 and you want to know what that initial number is.
To solve this problem you multiply 27 by 100 and then divide the total by 45 as follows: (27 x 100) / 45
When we put that into our calculator, we get the following answer:
60
Therefore, the answer to "27 is 45 percent of what number?" is 60, and you can also derive that 45 percent of 60 equals 27.
Hope it helps
Have a good day!
Which of the following describes the image of a triangle after a dilation that has a scale factor of 2/3?
A.-Each angle has 2/3 of the measure of its corresponding angle in the pre-image
B.-Each side has the same measure as its corresponding angle in the pre-image.
C.-Each angle has the same measure as its corresponding angle in the pre-image.
D.-Each side has 3/2 the length of its corresponding length in the pre-image.
We want to see which statement describes the image of a triangle after a dilation of scale factor of 2/3.
We will see that the correct option is C:
"Each angle has the same measure as its corresponding angle in the pre-image."
First, if we have a given figure and we apply a dilation of scale factor K, then all the measures of the given figures are affected by that dilation.
So if the 3 sides of the original triangle measured A, B, and C.
The new measures will be:
C' = k*CB' = k*BA' = k*ANotice that because all the sides changed proportionally, then the internal angles produced did not change after the dilation.
From this, we can conclude that the only correct option is C:
"Each angle has the same measure as its corresponding angle in the pre-image."
This says that the angles of the dilated triangle are the same ones as the angles of the initial triangle, which is true.
If you want to learn more, you can read:
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Identify the property that is used in each statement.
HELP ME PLEASE DUE IN 15 minutes!!!??
Answer:
65
Step-by-step explanation:
To join the school swim team, swimmers must be able to swim at least 480 yards
without stopping. Let n represent the number of yards a swimmer can swim without
stopping. Write an inequality describing which values of n will result in a swimmer
making the swim team.
a)
nis greater than or equal to 480
b) n is less than or equal to 480
n is greater than 480
d)
n is less than 480
Answer:
A) n is greater than or equal to 480.
Step-by-step explanation:
The keyword "at least" means greater than or equal to.
HELP IN THIS PLS I'LL DIRECTLY MARK YOU BRAINLIST!!]
Answer:
24 cars
Step-by-step explanation:
By using 11 cars and AED 79.75, you can find out the cost of washing 1 car.
(AED 79.75)/(11 cars) = AED 7.25 / car
Now we divide AED 174 by AED 7.25/car to find the number of cars.
(AED 174) / [(AED 7.25)/car] = (174/7.25) cars = 24 cars
Answer: 24 cars
(-8)–(-13)? Answer plz
Answer:
5
Step-by-step explanation:
(-8)-(-13)= 5
Yolanda ran three times last week. Here are the distances she ran (in kilometers).
3.99, 10, 6.4
What is the total distance Yolanda ran on these three days?
Answer:
20.03
Step-by-step explanation:
distance ran For 1st day+distance ran For 2nd day+distance ran For 3rd day.
3.99+10.6.4=20.03
You are given that a = 6.54 (to 3 significant figures) and b = 123 (to 3 significant figures).
Calculate upper and lower bounds for each of the following, give your answers to 3 significant figures:
(a) a + b
(b) ab
(c) a/b
(d) b - 1/a
The upper and lower bounds for the numbers are illustrations of approximation
How to calculate the upper and lower boundsThe numbers are given as:
a = 6.54 (to 3 significant figures)
b = 123 (to 3 significant figures)
(a) a + b
We have:
a + b = 6.54 + 123
a + b = 129.54
When approximated, the bounds to three significant digits are:
Lower bound = 129
Upper bound = 130.1
(b) ab
We have:
ab = 6.54 * 123
a + b = 804.42
When approximated, the bounds to three significant digits are:
Lower bound = 804
Upper bound = 805
(c) a/b
We have:
a/b = 6.54/123
a/b = 0.0531707317
When approximated, the bounds to three significant digits are:
Lower bound = 0.0531
Upper bound = 0.0532
(d) b - 1/a
We have:
b - 1/a = 123 - 1/6.54
b - 1/a = 122.847094801
When approximated, the bounds to three significant digits are:
Lower bound = 122
Upper bound = 123
Read more about approximation at:
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8 meters o om 16 meters
Answer:
2
Step-by-step explanation:
2000000000+2000000000
Answer:
its 4000000000
Step-by-step explanation:
add numbers
Answer:
2000000000+2000000000= 4000000000
is the square root of 23 rational or irrational